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Mud Hydraulics Optimization 89

4.3.2 Selecting the Flow Rate and the Bit Nozzle Size
For a given hole section to be drilled with a selected pump liner size, the
optimum mud flow rates and the nozzle sizes should be designed for dril-
ling at various depths until the end of the section. Traditionally, the flow
rate design has been performed graphically. It is a routine practice today
to carry out the design with computer programs.
The following procedure for selecting the optimum mud flow rate
and nozzle size is valid for the maximum bit hydraulic power and the
maximum jet impact force criteria. Based on the information presented
earlier in this chapter, it is clear that the optimum bit-to-pump pressure
ratio is Δp b = m for the maximum bit hydraulic power criterion and
p p m + 1
= for the maximum jet impact force criterion. From a practical
Δp b m
p p m + 2
standpoint, it is not always desirable to maintain the optimum pressure
ratio. At shallow depths, the flow rate usually is held constant at the max-
imum flow rate that can be achieved with the selected liner size. This
flow rate can be identified from the manufacturer’s specifications table
such as that shown in Table 3.6. If the table is not available for a given
pump horsepower rating P Hp , this maximum rate can be calculated by

1,714P Hp E
q max = (4.12)
p max

where
q max = maximum flow rate for the liner, psi or kPa
E = pump efficiency, dimensionless
p max = maximum allowable pump pressure for the liner, psi or kPa

This flow rate q max should be used until a critical depth is reached at
which Δp d = p p if the maximum bit hydraulic power criterion is used
m + 1
or Δp d = 2p p if the maximum jet impact force criterion is used. Before
m + 2
this critical depth is reached, the parasitic pressure loss can be calculated
using

Δp d = cq m (4.13)
max
and the pressure differential available for the bit is

Δp b = p max − cq m (4.14)
max